Have you already heard about the 17×17 Challenge ? It all started 7 months ago, and still no solution has been found. I have the feeling though that no really serious attempt at solving the problem has been done, even if very encouraging results have been found. It could be very interesting to keep track of the progress made so that results will be published here. Send what you have reached so far!
In the next few weeks, I will try to write about the Monte Carlo approaches described in the excellent book “Monte Carlo Strategies in Scientific Computing” by Jun Liu: I do not think that one can easily solve the problem with a direct implementation of these methods, but I want to know more about it. These are all more or less Markov Chain Monte Carlo Methods: I have tried the “parallel tempering” method, which gives results that are not that bad, and was planning to check the “flat histogram” method. “Simulated annealing” methods have succesfully been used to solve the Sudoku problem though: see Christian Robert blog for example. I am also planning to continue my reading of the fascinating book “Information, Physics, and Computation” by Marc Mezard: methods described in this book (belief propagation, k-SAT problem, etc…) are more adapted to the 17×17 challenge I think, and I am quite optimistic about it.